The first three multiples of 1153 all contain the digit 3: 1153, 2306, 3459. But its next multiple 4612 does not.

What is the smallest integer whose first four multiples all contain a 3?

What about 5 or 6 multiples?

(In reply to computer solution, taken beyond by Charlie)

There is no number such that its first 9 multiples contain a 3, but the number multiplied by 10 contains no 3. If the first 9 multiples of a number n contain a 3, then n*1=n contains a 3. Now, n*10 is n with a 0 at the end, so n*10 must contain a 3. That is why there is no solution for 9.

Posted by Math Man on 2017-01-31 20:34:54